Issue 48

D. Alexiane et alii, Frattura ed Integrità Strutturale, 48 (2019) 70-76; DOI: 10.3221/IGF-ESIS.48.09





(1)

τ  τ exp  

  γσ / kT U  

 



0

0

where:  is the time to failure,  0 is the binding energy on the atomic scale,  is a parameter proportional to the disorientation of the molecular structure, k is the Boltzmann’s constant, and T the absolute temperature. This equation has been validated for a wide variety of materials such as metals, alloys, non- metallic crystals, and polymers; nevertheless, when the time to failure is large enough, this equation ignores the reforming of atomic bonds and is not valid [22  . Quasi-brittle materials, including rocks, may fail under subcritical loading [23, 24  . Granite is characterized as coarser-grained crystalline rocks, which fatigue repeatability under three point bending tensile tests is characterized by random variation [25, 26  ; nevertheless, ultrasonic fatigue endurance obtained in this paper for the tested granite specimens shows a typical evolution in the S-N graph, as illustrated in Fig. 4. The repeatability on ultrasonic fatigue results here reported may be associated with the concentrated applied load at the center of the specimen, under this modality of very high frequency and low amplitude loading. The fracture of testing specimen quasi perpendicular to its length, Fig. 6, would be related to such repeatability too. In order to correlate the temperature variation during testing with the crack initiation and propagation, acoustic emission (AE), tests were carried out. The PAC system 18-bit A/D from MISTRAS Group, with 1kHz - 3MHz of scanning frequency was used for this purpose. The calibration for the acoustic emission tests was obtained following a procedure reported in ref. [27  . In Fig. 7 the frequency of elastic shocks recorded by AE (events rate/second) is plotted in the vertical axis against the time of ultrasonic fatigue test, in the horizontal axis. The results shown in this figure correspond to the lower applied load of 15.5 MPa with a testing time of approximately 16 seconds. is the period of the natural oscillation of atoms in the solid, U 0

Figure 7 : Frequency of elastic shock against time of ultrasonic fatigue life of approximately 16 sec.

Four stages are clearly distinguished during ultrasonic fatigue testing: the first stage, named phase I, is characterized by a noticeably increase of AE immediately after applying the load; the second stage is related to the gradually reduction of event rate (phase II). The third stage (phase III), which begins roughly at half of fatigue life, shows an exponential increase of the event rate, whereas in the last stage (phase IV), an import increase of event rate is observed before fracture. The four described stages during ultrasonic fatigue testing are related to the stages of the temperature on the granite specimen, recorded by the thermographic camera. Temperature increases rapidly at the first stage (phase I of AE), following by a quasi- steady state of temperature during the second stage (phase II of AE), and an increase of temperature during the third and fourth stages (phase III and phase IV of AE). Acoustic and thermographic analysis simultaneously may be used to predict the fatigue life of testing specimens [28  .

74